"James is making concrete using cement, sand and grave, in the ratio 1:2:3. James has:
63kg cement
112kg sand
210kg gravel
What is the max amount of concrete James can make?"
i wrote down the answer, but have totally forgotten how to get there!! i would be grateful for some help :))
210 kg gravel needs 70 kg cement, too much gravel
112 kg sand needs 56 kg cement, too much cement
The 112 sand is the limiter
so
56 kg cement
112 kg sand
168 kg gravel (3*56)
56 + 112 + 168 = total concrete
Well, James seems to have a whole lot of cement, sand, and gravel! Let's see if we can figure out the maximum amount of concrete he can make with those ingredients.
Now, since the ratio of cement to sand to gravel is 1:2:3, we can think of it as a recipe. That means for every part of cement, we need two parts of sand and three parts of gravel.
To find out how much concrete James can make, we need to determine the limiting ingredient. This is the ingredient that James has the least amount of compared to the ratio.
So, let's check which ingredient is the limiting one.
For cement, he has 63kg, which means he can make 63kg of concrete.
For sand, he has 112kg. Since we need two parts of sand to make one part of cement, we divide 112kg by 2. That gives us 56kg, which is less than 63kg. So sand is the limiting ingredient here.
Finally, for gravel, he has 210kg. Since we need three parts of gravel to make one part of cement, we divide 210kg by 3. That gives us 70kg, which is also less than 63kg. Hence, gravel is the limiting ingredient too.
Since both sand and gravel are limiting ingredients, we have to take the smaller amount they can produce, which is 56kg.
So, James can make a maximum of 56kg of concrete with the given amounts of cement, sand, and gravel. I hope that helps! And remember, even if you're short on concrete, laughter can always fill in the gaps. Keep smiling!
tysmm!
I don't get it
To find the maximum amount of concrete that James can make, we need to determine which material will run out first, as that will limit the amount of concrete he can produce.
Given that the ratio of cement, sand, and gravel is 1:2:3, we can assume that for every 1 part of cement, we will need 2 parts of sand and 3 parts of gravel.
Let's start by finding the amount of concrete James can make based on the cement he has:
1. Since the ratio of cement to concrete is 1:1, James can make a maximum of 63 kg of concrete using 63 kg of cement.
Next, let's consider the amount of sand James has and calculate the maximum concrete he can make based on that:
2. The ratio of sand to cement is 2:1. So, for every 2 parts of sand, we need 1 part of cement.
- Since James has 112 kg of sand, we calculate the amount of concrete he can make using this sand by dividing it by 2.
- 112 kg of sand / 2 = 56 kg of concrete
Now, let's analyze the amount of gravel James has and determine the maximum concrete he can make based on that:
3. The ratio of gravel to cement is 3:1. Therefore, for every 3 parts of gravel, we need 1 part of cement.
- Given that James has 210 kg of gravel, we calculate the amount of concrete he can make using this gravel by dividing it by 3.
- 210 kg of gravel / 3 = 70 kg of concrete
To determine the maximum amount of concrete James can produce, we take the minimum value obtained from the three calculations we made. In this case, the values are: 63 kg, 56 kg, and 70 kg.
Thus, the maximum amount of concrete James can make is 56 kg.
Therefore, James can make a maximum of 56 kg of concrete using the given amounts of cement, sand, and gravel.